Tensor ghosts in the inflationary cosmology

Abstract

Theories with curvature-squared terms in the action are known to contain ghost modes in general. However, if we regard curvature-squared terms as quantum corrections to the original theory, the emergence of ghosts may be simply due to the perturbative truncation of a full non-perturbative theory. If this is the case, there should be a way to live with ghosts. In this paper, we take the Euclidean path integral approach, in which ghost degrees of freedom can be, and are integrated out in the Euclideanized spacetime. We apply this procedure to Einstein gravity with a Weyl curvature-squared correction in the inflationary background. We find that the amplitude of tensor perturbations is modified by a term of O(α2H2) where α2 is a coupling constant in front of the Weyl-squared term and H is the Hubble parameter during inflation.